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Seasonal herbivory and mortality compensation in a swan–pondweed system
Ecological Modelling 147 (2002) 209– 219 www.elsevier.com/locate/ecolmodel
Seasonal herbivory and mortality compensation in a swan–pondweed system Niclas Jonze´n a,*, Bart A. Nolet b, Luis Santamarı´a b, Mats G.E. Svensson c a
b
Department of Theoretical Ecology, Ecology Building, Lund Uni6ersity, S-223 62 Lund, Sweden Netherlands Institute of Ecology (NIOO-KNAW), Centre for Limnology, PO Box 1299, 3600 BG Maarssen, The Netherlands c Department of Chemical Engineering, Lund Institute of Technology, Box 124, S-221 00 Lund, Sweden Received 10 October 2000; received in revised form 4 April 2001; accepted 18 July 2001
Abstract Many birds feed on submerged macrophytes during a temporally discrete period every year, for instance during migratory stopover or at the wintering grounds. Hence, seasonal herbivory is a common feature of the life cycle in many aquatic macrophytes. We are interested in the effect of Bewick’s swans (Cygnus columbianus bewickii ) feeding on the tubers of fennel pondweed (Potamogeton pectinatus) in the Netherlands every autumn. For that purpose, we developed a sequential macrophyte population model, including seasons of tuber production, herbivory and winter mortality as distinct and unambiguously defined events. The model is characterised and parameterised with both field and laboratory data. Tuber consumption inevitably decreases the density of ramets sprouting next spring, but it may actually increase the density of tubers produced in the following autumn. Hence, we can only understand the effect of grazing on the fennel pondweed population by recognising the seasonal structure of density-dependence. The mean density of fennel pondweed and the yield taken by swans are dependent on the foraging threshold below which no grazing takes place. Furthermore, the consumption has a stabilising effect for a wide range of parameter values. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Aquatic macrophytes; Cygnus columbianus; Functional response; Potamogeton pectinatus; Sequential density-dependence
1. Introduction Submerged macrophytes are thought to play a key role in many freshwater communities (Carpenter and Lodge, 1986; Scheffer, 1990; Jeppesen et al., 1997). Among others, they form an important food source for waterbirds. The nutrient rich * Corresponding author. Tel.: + 46-46-222-4142; fax: + 4646-222-3766. E-mail address: [email protected] (N. Jonze´n).
tubers of fennel pondweed, for instance, are the main food source for many waterbirds during moult and migration, both in Europe and North America (Anderson and Low, 1976; Beekman et al., 1991; Nolet and Drent, 1998). However, the knowledge on how grazing waterbirds affect the abundance, distribution and dynamics of submerged macrophytes is still limited (Lodge, 1991; Søndergaard et al., 1996). Most studies have been designed as exclosure/enclosure experiments, where grazed plots are compared with plots pro-
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tected from grazing. The results of the majority of these studies are ambiguous because most of the experiments were continued for less than a year, as pointed out by Idestam-Almquist (1996). Furthermore, the few ‘long-term’ studies conducted (i.e. 1–3 years) do not reveal any clear pattern, probably because different parts of the plants (e.g. shoots and tubers) had been grazed or because the measurements reflected the collective effect of selective grazing per se and indirect biomass loss caused by plant fragmentation during grazing (e.g. ‘destructive grazing behaviour’ by swans, geese, coots and ducks; Søndergaard et al., 1996). Fluctuations in herbivory occur on diurnal, seasonal and multiannual scales (Huntly, 1991). Because seasonality is a potential source of time delayed density-dependence (Kot and Schaffer, 1984; Oksanen, 1990) and therefore potentially of importance to the interannual population dynamics, some effort has been allocated to the study of seasonal patterns and their effects on food chains and communities (Fretwell, 1972; Oksanen, 1990; Hamba¨ ck, 1998). Many plant populations, including some submerged macrophytes, have different phases or life stages within the yearly life cycle. These phases often experience different events that may be density-dependent (Watkinson, 1980). If a population can be described by a sequence of density-dependent events, there exists a potential for a complex variety of dynamics (A, stro¨ m et al., 1996). The importance of explicitly taking the temporal order into account has been recognised by entomologists (e.g. Sota, 1988; Iwasa et al., 1992; Holt and Colvin, 1997) and has had some practical applications as well (Allen et al., 1991). Recently, Jonze´ n and Lundberg (1999) concluded that the temporal ordering of events may not only have profound influences on the dynamics, but will also affect whether a source of mortality will be additive or compensatory. That will have implications for when the effects of a source of mortality, for instance grazing, are to be evaluated (Boyce et al., 1999). Furthermore, the temporal ordering of events will influence the investment strategies in asexual and sexual reproduction (Hemborg, 1998). To our knowledge, these insights have not been taken into account when
studying annual and pseudo-annual plant populations and plant–herbivore interactions. In this paper, we take a broad approach, combining data from the field and the laboratory with mathematical modelling. We develop a simple and time-structured discrete-time model specified to characterise a plant population with a pseudo-annual life cycle. Every year the plant population experiences three discrete periods of growth and reproduction, herbivory-related mortality and over-wintering mortality. We use this model to analyse the interaction between Bewick’s swans (Cygnus columbianus bewickii Yarrel) and fennel pondweed (Potamogeton pectinatus L.) in the Netherlands. This system is endowed with many of the characteristics of the model. The potential effects of seasonal herbivory on mean densities and stability conditions of ramets, tubers and, finally, the yield taken by swans are investigated.
2. Material and methods
2.1. Study system The Lauwersmeer (Netherlands; 53°22% N, 06°13% E) is a shallow freshwater lake (750 ha) that contains extensive beds of fennel pondweed. This submerged macrophyte is a pseudo-annual that survives the winter in the form of belowground tubers. The growth season takes place from mid April to September, and tubers are produced from July to September. This lake is one of the most important autumn stopovers of migrating Bewick’s swans in the Netherlands. During their return from their breeding grounds in the arctic tundra (Russia), Bewick’s swans start feeding on fennel pondweed upon arrival in the Lauwersmeer in October and November (Beekman et al., 1991). The swans dig pits by trampling with their feet, dip their head and neck below water or up-end to reach the tubers, and extract the tubers from the soil upon touch by sieving the sediment through the bill. The rather small tubers (length: 1–20 mm) contain great levels of highly digestible carbohydrates, which presumably can easily be converted into fat reserves. This proba-
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bly explains the swans’ preference for this food source during the energy-demanding migration. After a few weeks the swans switch to harvest leftovers of sugarbeet or move further south (Beekman et al., 1991).
2.2. The general model Let Nspring denote the number of ramets sprouting (from tubers) in spring, Nautumn the number of tubers produced and Nwinter the number of tubers left after grazing. If we further let Nautumn be a function f1 of Nspring, Nwinter a function f2 of Nautumn, and Nspring a function f3 of Nwinter, the life cycle can be modelled as N(t +1)spring = f3{ f2{ f1{N(t)spring}}} (Fig. 1). The functions f1, f2, f3 are defined below. The swans’ foraging decisions are assumed to be based on tuber biomass rather than numbers. Tuber biomass is expressed as dry weight (DW; after 2 days at 70 °C).
2.3. Parameter estimation and the specific model Characteristics of the tuber production were measured in summer exclosures in 1997. The ex-
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closures prevented feeding by ducks and coots on seeds and leaves. The maximum per capita tuber production (i) and the strength of density-dependence (b) were estimated from the relationship between the per capita tuber production counted in October against the planting density (number of tubers m − 2) in pots burrowed in the sediment and placed within the exclosures. Hence, the estimated tuber production implicitly includes the possible effects of self-thinning during summer. This simplification is valid because, in this study, we are not interested in ramet growth or biomass per se. The per capita tuber production is defined as P(Nspring)= i exp(− bNspring)
(1)
where i is the maximum per capita tuber production, b is the strength of density-dependence and Nspring denotes the density of ramets. This model was preferable to a linear model (e.g. the logistic growth model) because it minimises the sum of squares with the same number of parameters as the linear model (Hilborn and Mangel, 1997). Our general results, however, are not dependent on the exact form of density dependence.
Fig. 1. The model life-cycle of fennel pondweed. In spring, the population consists entirely of ramets. The function P(Nspring) describes how per capita tuber production is related to ramet density (Nspring). After tuber production, the ramets die and Nautumn and Nwinter are the population densities of tubers before and after grazing. The function G(Nautumn) describes the total tuber mortality due to swan grazing. Finally, M(Nwinter) relates the per capita rate of tuber mortality to tuber density after grazing.
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The parameter values estimated in the field experiment were in the range 35i 5 8 and 0.00135b5 0.07 (Santamarı´a, Unpublished data). The estimated values of i are far below what has been found in laboratory and commongarden studies (e.g. i varied between 5 and 80 tubers plant − 1 in a common garden experiment where initial tuber size varied between 10 and 190 mg; Santamarı´a, Unpublished data), but these plants grow under atypical, ideal conditions (high nutrient supply, low turbidity, wind shelter). Sampling tubers in November and March/April over a 3-year period in a non-experimental set-up in the Lauwersmeer (see Nolet et al., 2001) gave an average per capita tuber production between 3 and 9 (Nolet, Unpublished data). Thus, the estimate of i from the field experiment was more typical for average rather than maximum values. We suspect that this happened because (a) the lowest experimental density was rather high (equivalent to 16 plants m − 2) and (b) the growth potential of the experimental plants may have been reduced by shading by surrounding, non-experimental plants. Therefore, we present in the results the output from simulations over a relevant range of parameter values. The per capita risk of tuber mortality due to grazing by swans is assumed to be dependent on the tuber density before grazing. More explicitly, we assume that there exists a threshold tuber density below which no foraging takes place. Hence, if the tuber density before grazing (Nautumn) is less than this foraging threshold, f in the model below, no tubers will be removed from the population. On the other hand, if Nautumn \f, a fraction (h in the model) of the difference between Nautumn and f will be removed by the swans. This fraction h is called the maximum depletion since it approaches the actual fraction of the tubers eaten by swans when Nautumn goes to infinity. The total number of tubers eaten by the swans as a function of the tuber density before grazing becomes
Brown, 1990) as well as empirical evidence from our study system (Nolet et al., 2001). Tuber mortality due to swan grazing was measured in the autumn of 1996 and 1997. Seventeen plots were sampled and classified as sandy-shallow, sandy-deep, clayey-shallow and clayey-deep. We assessed the effect of plot category on the swan consumption (i.e. the difference between initial and final tuber density per plot) in an analysis of covariance with the initial tuber density as a co-variable. The x-intercepts of the lines regressing consumption on initial tuber density gave estimates of the minimum giving-up density (GUD) per category— that equals the foraging threshold in the present study— and the slope of these lines corresponds to the maximum depletion (h). For further details, see Nolet et al. (2001). The estimates of GUD were in the range 6.35 GUD 5 30.6 g DW m − 2 depending on plot category and we used these estimates to choose an appropriate range of values of the foraging threshold ( f ) in our model. Furthermore, the maximum depletion (h) was estimated to 0.869 0.10 S.E. and 0.759 0.19 S.E. in 1996 and 1997, respectively. In our model, we let f and h vary over a wide range of values covering the empirical estimates. The swans’ foraging decisions are assumed to be based on tuber biomass rather than number, but tuber production is dependent on the ramet density in numbers. Therefore, we divided the tuber biomass by the mean weight of a tuber (w), set to 0.03 g (Santamarı´a, Unpublished data), to be able to express the mean densities and the yield taken by swans in both numbers m − 2 and g DW m − 2. We also investigated the model output for a range of w-values, 0.0065 w50.05, without any qualitative differences found. Tuber winter mortality from other causes than swan grazing was measured to on average 21% in winter exclosures (Santamarı´a, Unpublished data). Based on these data, the per capita mortality rate of tubers was assumed to be density-independent and of the magnitude 20%, hence,
G(Nautumn)= h(Nautumn −f )
M(Nwinter)= m=0.2
(2)
This type of functional response is supported by a strong theoretical underpinning (Mitchell and
(3)
Putting the different processes together results in the following model life-cycle:
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Fig. 2. Mean population density in spring (N*spring = ramet density), autumn (N*autumn =tuber density) and winter (N*winter =tuber density) as a function of the maximum depletion (h) used by the swans. h is the slope of the functional response and approaches the actual fraction of tubers taken as the tuber density before grazing goes to infinity. The foraging threshold ( f ) —the tuber density below which no foraging takes place —is set to 7 g m − 2 (panels a – c) or 14 g m − 2 (panels d – f). The maximum per capita tuber production (i), is either 5 (solid curves), 10 (dashed curves) or 15 (dotted curves). Other parameter values are b =0.006 (strength of density-dependence), m= 0.2 (the per capita mortality rate of tubers during winter), and mean tuber weight (w) =0.03 g.
N(t + 1)spring = N(t)springi exp( −bN(t)spring) − h(N(t)autumn −f ) − mN(t)winter (4) where N(t)autumn N(t)springi exp( − bN(t)spring) and N(t)winter N(t)autumn −h(N(t)autumn −f ). We simulated Eq. (4) for 200 generations and removed the impact of transients by discarding the first 100 generations. We then calculated the mean density of the last 100 generations for the number of sprouting ramets (Nspring), the number of tubers produced (Nautumn) and the number of tubers left after grazing (Nwinter). We will present the mean densities also when the underlying dynamics is oscillatory. To focus on statistics of location such as mean values is natural when studying compensation and average effects in de-
terministic as well as stochastic systems. Furthermore, it also facilitates the comparison between different aspects of grazing. However, to better expose the underlying non-linear dynamics we also present a phase diagram, where the dynamic properties are revealed for combinations of maximum per capita tuber production (i) and maximum depletion (h).
3. Results The effect of swan grazing may be different for different life stages (ramets and tubers), which occur at different times of the year (Fig. 2). Where as the mean density of ramets (N*spring) and the mean density of tubers after grazing (N*winter)
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decreased with increasing maximum depletion by swans, the mean tuber density before grazing (N*autumn) actually increased. The discontinuous curves in panels d–f indicate a transition from a stable equilibrium (when h exceeds a critical value) to a two-point cycle (when h is below that critical value). The foraging threshold ( f ) had a major impact on the mean densities (Fig. 3), but the exact pattern depended on the maximum depletion. This means that the level of depletion of the tubers by the swans in a particular autumn greatly affected the mean number of tubers available to the swans in the next autumn. Fig. 4 shows the yield taken by the swans for different foraging threshold ( f ), i-values and the
maximum depletion (h). Because the yield is directly related to the tuber production, the effect on the yield is similar to the effect on N*autumn. Fig. 5 demonstrates the yield as a function of tuber winter mortality (m) for different i-values and foraging threshold ( f ). For a wide range of winter mortality, there is barely any effect on N*autumn and N*winter. There is, naturally, a rather strong negative effect of increased winter mortality on the number of sprouting ramets the following spring (N*spring). In Fig. 6, we show the effect of the maximum per capita tuber production (i) and the maximum depletion (h) on the stability of the population, as a phase diagram of ramet density in spring. In general, increasing i is destabilising in the sense
Fig. 3. Mean population density in spring (N*spring = ramet density), autumn (N*autumn =tuber density) and winter (N*winter =tuber density) plotted against the foraging threshold (the tuber density below which no foraging takes place). The maximum depletion (h) is set to 1 (solid curves), 0.8 (dashed curves) or 0.6 (dotted curves). h is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The maximum per capita tuber production (i) is either 5 (a – c), 10 (d – f), or 15 (g –i). Other parameter values are b =0.006 (strength of density-dependence), m =0.2 (the per capita mortality rate of tubers during winter) and w =0.03 g (mean tuber weight). When the tuber density before grazing falls below the foraging threshold (intersects the straight line in panels d –f and indicated by arrows in all panels), no grazing takes place. In the lower panels (g – i), however, the population is cyclic and grazing occurs every second year even though the mean density (N*autumn) is below the foraging threshold.
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Fig. 4. Yield taken by the swans as a function of the foraging threshold ( f ), i.e. the tuber density below which no foraging takes place. The maximum depletion (h) is either 1 (solid curves), 0.8 (dashed curves) or 0.6 (dotted curves). h is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The maximum per capita tuber production (i) is 5 (a), 10 (b), or 15 (c). Other parameter values are b = 0.006 (strength of density-dependence), m =0.2 (the per capita mortality rate of tubers during winter), and w= 0.03 g (mean tuber weight).
that increasing i results in a transition from stable to cyclic and, finally, chaotic dynamics. Increasing h, on the other hand, has a dampening effect on the dynamics. There is no qualitative, and barely any quantitative, difference between the effect on population density at different times of the year.
4. Discussion Since waterbirds consume the whole tuber, herbivory on tubers is in many respects similar to predation. In that sense, we are studying a special case of herbivory, different from partial consumption of leaves and shoots (A, stro¨ m et al., 1990). A decrease in ramet density with increasing grazing, as predicted by our model, has been found in the one study in which ramet density was
measured (Idestam-Almquist, 1996). However, the potential for compensatory tuber production as predicted by the model, has not been observed or suggested before. The predicted increase in tuber density from our model is a consequence of the negative density-dependence in the per capita tuber production. The swans simply remove tubers before the tubers give rise to crowding effects during the reproductive season. In contrast, Anderson and Low (1976) reported a lower tuber density in open plots relative to adjacent exclosures. Both Anderson and Low (1976) and Idestam-Almquist (1996) used exclosures that were present year-round, and thus excluded both leaf- and tuber-eating waterbirds. In our present study we explicitly considered grazing by tubereating swans only. Inclusion of summer grazing would add further complexity to this swan– pondweed interaction. Summer exclosure experi-
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ments in the Lauwersmeer have shown that an increase in grazing by leaf-eating coots (Fulica atra) leads to a reduction of tuber density in the following autumn (Santamarı´a, Unpublished data). Our results show that it is somewhat trivial to conclude that herbivory reduces resource density by measuring density before and just after grazing has occurred, because the mortality can be compensated for by one or several density-dependent processes following it. To understand the potential effects of a source of mortality (e.g. herbivory) on the resource density, the temporal structure of density-dependent events becomes important (A, stro¨ m et al., 1996; Kokko and Lindstro¨ m, 1998; Jonze´ n and Lundberg, 1999). Also the timing of the evaluation of the effects in relation to different processes becomes critical if mortality
and production are seasonal events (Boyce et al., 1999; Jonze´ n and Lundberg, 1999). This illustrates the need to measure how the per capita mortality and production rates vary with density if we want to make progress in our understanding of population dynamics in general and consumer–resource interactions in particular. Unfortunately, this is often the one feature of a plant population that is not investigated during demographic studies (Watkinson, 1980). The model structure presented here represents a framework for evaluating data on demographic rates and examine ramifications for population dynamics (Boyce et al., 1999). In fact, for the kind of data we have got (no time series, but data on seasonal processes) there is simply no other model structure to consider but an explicit seasonal model. There are different ways of modelling sea-
Fig. 5. Mean population density in spring (N*spring = ramet density; panel a), autumn (N*autumn =tuber density; panel b) and winter (N*winter =tuber density; panel c) plotted against per capita mortality rate of tubers during winter (m). Solid curves: i= 5, f= 7; dashed curves: i= 5, f= 14; dashed/dotted curves: i =15, f =7; dotted curves: i= 15, f= 14 (i is the maximum per capita tuber production and f is the foraging threshold, i.e. the tuber density below which no foraging takes place). Other parameter values are b= 0.006 (strength of density-dependence), h= 0.8 (maximum depletion, the slope of the functional response), and w =0.03 g (mean tuber weight).
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Fig. 6. Phase diagram for the population density in spring ( = ramet density). The maximum depletion (h) is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The foraging threshold ( f ) —the tuber density below which no foraging takes place —is set to 7 g m − 2. Other parameter values are b= 0.006 (strength of density-dependence), m= 0.2 (the per capita mortality rate of tubers during winter), and w =0.03 g (mean tuber weight).
sonality. A common approach is to use differential equations and replace a parameter with a periodic function. That approach was used by Holt and Colvin (1997) who showed that a correct description of seasonality was necessary to reconstruct the observed population dynamics in an African grasshopper. A similar approach was used also by Kokko and Lindstro¨ m (1998) in a harvesting context. We think, however, that including seasonality as discrete events— as in our study—is more intuitive and facilitates the interpretation of data. Under what circumstances a consumer has a stabilising or destabilising effect on a resource has been a matter of debate for quite some time (e.g. Schmitz et al., 1997). The key to understanding has been the functional response, i.e. the per predator predation rate as a function of prey density (Holling, 1959). The functional response offers an attractive possibility to link behavioural ecology and population/community dynamics
(Fryxell and Lundberg, 1998). The functional response used in this study conforms to the optimal functional response, i.e. the classical so-called differential functional response integrated over both foraging time and alternative activities when time is allocated optimally (Abrams, 1982; Sih, 1984; Abrams, 1990; Mitchell & Brown, 1990). If there exists a threshold density, below which no consumption occurs, there always exists a range of densities over which the consumption is stabilising (Mitchell and Brown, 1990). When the yield is only a function of the net energetic gain, the slope of the optimal functional response is predicted to be one over this range. There is more than one possible explanation for a slope less than one (underutilization of rich patches), as was found by Nolet et al. (2001) and used in our study. First, foraging might incur an extra cost, termed the missed opportunity cost of foraging (Mitchell and Brown, 1990). Second, the birds only possess incomplete knowledge about
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their resources (Valone and Brown, 1989). Third, patches of similar quality are spatially grouped (Morgan et al., 1997). Which of the three plays the most important role in our system is impossible to say at the moment. During winter, the tubers suffer from mortality. The different effect of increasing winter mortality on the mean density of ramets (N*spring decreases with increasing m) and tubers (small effect for a wide range of m) again highlights the non-trivial task of evaluating the effect of seasonal population processes. The process of winter mortality, however, deserves further study. Recently, Idestam-Almquist (1996) found a severe effect of waterfowl on fennel pondweed abundance and suggested that waterfowl may stabilise a plant population at a low density. This idea is supported by our study, considering the foraging threshold and maximum depletion found, which tend to have a stabilising effect. In contrast, the swans only depend on fennel pondweed tubers during migration, so other factors than local tuber density are likely to affect swan numbers. The swan dynamic is also operating at a very different (slower) time scale than the tuber population. We thus assumed that the influence of the plant population on the swan population is insignificant. Such an asymmetry of the interaction between consumers and resources is not unusual in many plant– herbivore systems (Fryxell and Lundberg, 1998).
5. Conclusion We have clearly demonstrated the potential importance of explicitly taking seasonality into account when trying to understand how herbivory affects plant dynamics. This is so independent on whether we are building models for scientific or management purposes, or if we are trying to interpret experimental data. This has recently been highlighted in a predation and management context (Boyce et al., 1999), but this line of thinking has, to our knowledge, not yet permeated the herbivory literature. This general conclusion is nicely illustrated by the swan– pondweed system we have studied, where the pondweed seems to be
able to sustain heavy grazing due to compensatory tuber production.
Acknowledgements We are grateful to Wolf Mooij, Marcel Klaassen, Miguel Rodrı´guez-Girone´ s, Anna Ga˚ rdmark and Per Lundberg for invaluable comments and suggestions. Niclas Jonze´ n was financially supported by grants from the Swedish Research Council for Forestry and Agriculture and the Royal Netherlands Academy of Arts and Sciences. This is NIOO-KNAW publication 2830 of the Netherlands Institute of Ecology.
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Lodge, D.M., 1991. Herbivory on freshwater macrophytes. Aquat. Bot. 41, 195 – 224. Mitchell, W.A., Brown, J.S., 1990. Density-dependent harvest rates by optimal foragers. Oikos 57, 180 – 190. Morgan, R.A., Brown, J.S., Thorson, J.M., 1997. The effect of spatial scale on the functional response of fox squirrels. Ecology 78, 1087 – 1097. Nolet, B.A., Drent, R.H., 1998. Bewick’s Swans refuelling on pondweed tubers in the Dvina Bay (White Sea) during their spring migration: first come, first served. J. Avian Biol. 29, 574 – 581. Nolet, B.A., Langevoord, O., Bevan, R.M., Engelaar, K.R., Klaassen, M., Mulder, R.J.W., Van Dijk, S., 2001. Spatial variation in tuber depletion by swans explained by differences in net intake rates. Ecology 82, 1655 – 1667. Oksanen, L., 1990. Exploitation of ecosystems in seasonal environments. Oikos 57, 14 – 24. Scheffer, M., 1990. Multiplicity of stable states in freshwater systems. Hydrobiologia 200/201, 475 – 487. Schmitz, O.J., Beckerman, A.P., Litman, S., 1997. Functional responses of adaptive consumers and community stability with emphasis on the dynamics of plant – herbivore systems. Evol. Ecol. 11, 773 – 784. Sih, A., 1984. Optimal behavior and density-dependent predation. Am. Nat. 123, 314 – 326. Sota, T., 1988. Univoltine and bivoltine life cycles in insects: a model with density-dependent selection. Res. Popul. Ecol. 30, 135 – 144. Søndergaard, M., Bruun, L., Lauridsen, T., Jeppesen, E., Madsen, T.V., 1996. The impact of grazing waterfowl on submerged macrophytes: In situ experiments in a shallow eutrophic lake. Aquat. Bot. 53, 73 – 84. Valone, T.J., Brown, J.S., 1989. Measuring patch assessment abilities of desert granivores. Ecology 70, 1800 – 1810. Watkinson, A.R., 1980. Density-dependence in single-species populations of plants. J. Theor. Biol. 83, 345 – 357.
Seasonal herbivory and mortality compensation in a swan–pondweed system Niclas Jonze´n a,*, Bart A. Nolet b, Luis Santamarı´a b, Mats G.E. Svensson c a
b
Department of Theoretical Ecology, Ecology Building, Lund Uni6ersity, S-223 62 Lund, Sweden Netherlands Institute of Ecology (NIOO-KNAW), Centre for Limnology, PO Box 1299, 3600 BG Maarssen, The Netherlands c Department of Chemical Engineering, Lund Institute of Technology, Box 124, S-221 00 Lund, Sweden Received 10 October 2000; received in revised form 4 April 2001; accepted 18 July 2001
Abstract Many birds feed on submerged macrophytes during a temporally discrete period every year, for instance during migratory stopover or at the wintering grounds. Hence, seasonal herbivory is a common feature of the life cycle in many aquatic macrophytes. We are interested in the effect of Bewick’s swans (Cygnus columbianus bewickii ) feeding on the tubers of fennel pondweed (Potamogeton pectinatus) in the Netherlands every autumn. For that purpose, we developed a sequential macrophyte population model, including seasons of tuber production, herbivory and winter mortality as distinct and unambiguously defined events. The model is characterised and parameterised with both field and laboratory data. Tuber consumption inevitably decreases the density of ramets sprouting next spring, but it may actually increase the density of tubers produced in the following autumn. Hence, we can only understand the effect of grazing on the fennel pondweed population by recognising the seasonal structure of density-dependence. The mean density of fennel pondweed and the yield taken by swans are dependent on the foraging threshold below which no grazing takes place. Furthermore, the consumption has a stabilising effect for a wide range of parameter values. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Aquatic macrophytes; Cygnus columbianus; Functional response; Potamogeton pectinatus; Sequential density-dependence
1. Introduction Submerged macrophytes are thought to play a key role in many freshwater communities (Carpenter and Lodge, 1986; Scheffer, 1990; Jeppesen et al., 1997). Among others, they form an important food source for waterbirds. The nutrient rich * Corresponding author. Tel.: + 46-46-222-4142; fax: + 4646-222-3766. E-mail address: [email protected] (N. Jonze´n).
tubers of fennel pondweed, for instance, are the main food source for many waterbirds during moult and migration, both in Europe and North America (Anderson and Low, 1976; Beekman et al., 1991; Nolet and Drent, 1998). However, the knowledge on how grazing waterbirds affect the abundance, distribution and dynamics of submerged macrophytes is still limited (Lodge, 1991; Søndergaard et al., 1996). Most studies have been designed as exclosure/enclosure experiments, where grazed plots are compared with plots pro-
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tected from grazing. The results of the majority of these studies are ambiguous because most of the experiments were continued for less than a year, as pointed out by Idestam-Almquist (1996). Furthermore, the few ‘long-term’ studies conducted (i.e. 1–3 years) do not reveal any clear pattern, probably because different parts of the plants (e.g. shoots and tubers) had been grazed or because the measurements reflected the collective effect of selective grazing per se and indirect biomass loss caused by plant fragmentation during grazing (e.g. ‘destructive grazing behaviour’ by swans, geese, coots and ducks; Søndergaard et al., 1996). Fluctuations in herbivory occur on diurnal, seasonal and multiannual scales (Huntly, 1991). Because seasonality is a potential source of time delayed density-dependence (Kot and Schaffer, 1984; Oksanen, 1990) and therefore potentially of importance to the interannual population dynamics, some effort has been allocated to the study of seasonal patterns and their effects on food chains and communities (Fretwell, 1972; Oksanen, 1990; Hamba¨ ck, 1998). Many plant populations, including some submerged macrophytes, have different phases or life stages within the yearly life cycle. These phases often experience different events that may be density-dependent (Watkinson, 1980). If a population can be described by a sequence of density-dependent events, there exists a potential for a complex variety of dynamics (A, stro¨ m et al., 1996). The importance of explicitly taking the temporal order into account has been recognised by entomologists (e.g. Sota, 1988; Iwasa et al., 1992; Holt and Colvin, 1997) and has had some practical applications as well (Allen et al., 1991). Recently, Jonze´ n and Lundberg (1999) concluded that the temporal ordering of events may not only have profound influences on the dynamics, but will also affect whether a source of mortality will be additive or compensatory. That will have implications for when the effects of a source of mortality, for instance grazing, are to be evaluated (Boyce et al., 1999). Furthermore, the temporal ordering of events will influence the investment strategies in asexual and sexual reproduction (Hemborg, 1998). To our knowledge, these insights have not been taken into account when
studying annual and pseudo-annual plant populations and plant–herbivore interactions. In this paper, we take a broad approach, combining data from the field and the laboratory with mathematical modelling. We develop a simple and time-structured discrete-time model specified to characterise a plant population with a pseudo-annual life cycle. Every year the plant population experiences three discrete periods of growth and reproduction, herbivory-related mortality and over-wintering mortality. We use this model to analyse the interaction between Bewick’s swans (Cygnus columbianus bewickii Yarrel) and fennel pondweed (Potamogeton pectinatus L.) in the Netherlands. This system is endowed with many of the characteristics of the model. The potential effects of seasonal herbivory on mean densities and stability conditions of ramets, tubers and, finally, the yield taken by swans are investigated.
2. Material and methods
2.1. Study system The Lauwersmeer (Netherlands; 53°22% N, 06°13% E) is a shallow freshwater lake (750 ha) that contains extensive beds of fennel pondweed. This submerged macrophyte is a pseudo-annual that survives the winter in the form of belowground tubers. The growth season takes place from mid April to September, and tubers are produced from July to September. This lake is one of the most important autumn stopovers of migrating Bewick’s swans in the Netherlands. During their return from their breeding grounds in the arctic tundra (Russia), Bewick’s swans start feeding on fennel pondweed upon arrival in the Lauwersmeer in October and November (Beekman et al., 1991). The swans dig pits by trampling with their feet, dip their head and neck below water or up-end to reach the tubers, and extract the tubers from the soil upon touch by sieving the sediment through the bill. The rather small tubers (length: 1–20 mm) contain great levels of highly digestible carbohydrates, which presumably can easily be converted into fat reserves. This proba-
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bly explains the swans’ preference for this food source during the energy-demanding migration. After a few weeks the swans switch to harvest leftovers of sugarbeet or move further south (Beekman et al., 1991).
2.2. The general model Let Nspring denote the number of ramets sprouting (from tubers) in spring, Nautumn the number of tubers produced and Nwinter the number of tubers left after grazing. If we further let Nautumn be a function f1 of Nspring, Nwinter a function f2 of Nautumn, and Nspring a function f3 of Nwinter, the life cycle can be modelled as N(t +1)spring = f3{ f2{ f1{N(t)spring}}} (Fig. 1). The functions f1, f2, f3 are defined below. The swans’ foraging decisions are assumed to be based on tuber biomass rather than numbers. Tuber biomass is expressed as dry weight (DW; after 2 days at 70 °C).
2.3. Parameter estimation and the specific model Characteristics of the tuber production were measured in summer exclosures in 1997. The ex-
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closures prevented feeding by ducks and coots on seeds and leaves. The maximum per capita tuber production (i) and the strength of density-dependence (b) were estimated from the relationship between the per capita tuber production counted in October against the planting density (number of tubers m − 2) in pots burrowed in the sediment and placed within the exclosures. Hence, the estimated tuber production implicitly includes the possible effects of self-thinning during summer. This simplification is valid because, in this study, we are not interested in ramet growth or biomass per se. The per capita tuber production is defined as P(Nspring)= i exp(− bNspring)
(1)
where i is the maximum per capita tuber production, b is the strength of density-dependence and Nspring denotes the density of ramets. This model was preferable to a linear model (e.g. the logistic growth model) because it minimises the sum of squares with the same number of parameters as the linear model (Hilborn and Mangel, 1997). Our general results, however, are not dependent on the exact form of density dependence.
Fig. 1. The model life-cycle of fennel pondweed. In spring, the population consists entirely of ramets. The function P(Nspring) describes how per capita tuber production is related to ramet density (Nspring). After tuber production, the ramets die and Nautumn and Nwinter are the population densities of tubers before and after grazing. The function G(Nautumn) describes the total tuber mortality due to swan grazing. Finally, M(Nwinter) relates the per capita rate of tuber mortality to tuber density after grazing.
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The parameter values estimated in the field experiment were in the range 35i 5 8 and 0.00135b5 0.07 (Santamarı´a, Unpublished data). The estimated values of i are far below what has been found in laboratory and commongarden studies (e.g. i varied between 5 and 80 tubers plant − 1 in a common garden experiment where initial tuber size varied between 10 and 190 mg; Santamarı´a, Unpublished data), but these plants grow under atypical, ideal conditions (high nutrient supply, low turbidity, wind shelter). Sampling tubers in November and March/April over a 3-year period in a non-experimental set-up in the Lauwersmeer (see Nolet et al., 2001) gave an average per capita tuber production between 3 and 9 (Nolet, Unpublished data). Thus, the estimate of i from the field experiment was more typical for average rather than maximum values. We suspect that this happened because (a) the lowest experimental density was rather high (equivalent to 16 plants m − 2) and (b) the growth potential of the experimental plants may have been reduced by shading by surrounding, non-experimental plants. Therefore, we present in the results the output from simulations over a relevant range of parameter values. The per capita risk of tuber mortality due to grazing by swans is assumed to be dependent on the tuber density before grazing. More explicitly, we assume that there exists a threshold tuber density below which no foraging takes place. Hence, if the tuber density before grazing (Nautumn) is less than this foraging threshold, f in the model below, no tubers will be removed from the population. On the other hand, if Nautumn \f, a fraction (h in the model) of the difference between Nautumn and f will be removed by the swans. This fraction h is called the maximum depletion since it approaches the actual fraction of the tubers eaten by swans when Nautumn goes to infinity. The total number of tubers eaten by the swans as a function of the tuber density before grazing becomes
Brown, 1990) as well as empirical evidence from our study system (Nolet et al., 2001). Tuber mortality due to swan grazing was measured in the autumn of 1996 and 1997. Seventeen plots were sampled and classified as sandy-shallow, sandy-deep, clayey-shallow and clayey-deep. We assessed the effect of plot category on the swan consumption (i.e. the difference between initial and final tuber density per plot) in an analysis of covariance with the initial tuber density as a co-variable. The x-intercepts of the lines regressing consumption on initial tuber density gave estimates of the minimum giving-up density (GUD) per category— that equals the foraging threshold in the present study— and the slope of these lines corresponds to the maximum depletion (h). For further details, see Nolet et al. (2001). The estimates of GUD were in the range 6.35 GUD 5 30.6 g DW m − 2 depending on plot category and we used these estimates to choose an appropriate range of values of the foraging threshold ( f ) in our model. Furthermore, the maximum depletion (h) was estimated to 0.869 0.10 S.E. and 0.759 0.19 S.E. in 1996 and 1997, respectively. In our model, we let f and h vary over a wide range of values covering the empirical estimates. The swans’ foraging decisions are assumed to be based on tuber biomass rather than number, but tuber production is dependent on the ramet density in numbers. Therefore, we divided the tuber biomass by the mean weight of a tuber (w), set to 0.03 g (Santamarı´a, Unpublished data), to be able to express the mean densities and the yield taken by swans in both numbers m − 2 and g DW m − 2. We also investigated the model output for a range of w-values, 0.0065 w50.05, without any qualitative differences found. Tuber winter mortality from other causes than swan grazing was measured to on average 21% in winter exclosures (Santamarı´a, Unpublished data). Based on these data, the per capita mortality rate of tubers was assumed to be density-independent and of the magnitude 20%, hence,
G(Nautumn)= h(Nautumn −f )
M(Nwinter)= m=0.2
(2)
This type of functional response is supported by a strong theoretical underpinning (Mitchell and
(3)
Putting the different processes together results in the following model life-cycle:
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Fig. 2. Mean population density in spring (N*spring = ramet density), autumn (N*autumn =tuber density) and winter (N*winter =tuber density) as a function of the maximum depletion (h) used by the swans. h is the slope of the functional response and approaches the actual fraction of tubers taken as the tuber density before grazing goes to infinity. The foraging threshold ( f ) —the tuber density below which no foraging takes place —is set to 7 g m − 2 (panels a – c) or 14 g m − 2 (panels d – f). The maximum per capita tuber production (i), is either 5 (solid curves), 10 (dashed curves) or 15 (dotted curves). Other parameter values are b =0.006 (strength of density-dependence), m= 0.2 (the per capita mortality rate of tubers during winter), and mean tuber weight (w) =0.03 g.
N(t + 1)spring = N(t)springi exp( −bN(t)spring) − h(N(t)autumn −f ) − mN(t)winter (4) where N(t)autumn N(t)springi exp( − bN(t)spring) and N(t)winter N(t)autumn −h(N(t)autumn −f ). We simulated Eq. (4) for 200 generations and removed the impact of transients by discarding the first 100 generations. We then calculated the mean density of the last 100 generations for the number of sprouting ramets (Nspring), the number of tubers produced (Nautumn) and the number of tubers left after grazing (Nwinter). We will present the mean densities also when the underlying dynamics is oscillatory. To focus on statistics of location such as mean values is natural when studying compensation and average effects in de-
terministic as well as stochastic systems. Furthermore, it also facilitates the comparison between different aspects of grazing. However, to better expose the underlying non-linear dynamics we also present a phase diagram, where the dynamic properties are revealed for combinations of maximum per capita tuber production (i) and maximum depletion (h).
3. Results The effect of swan grazing may be different for different life stages (ramets and tubers), which occur at different times of the year (Fig. 2). Where as the mean density of ramets (N*spring) and the mean density of tubers after grazing (N*winter)
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decreased with increasing maximum depletion by swans, the mean tuber density before grazing (N*autumn) actually increased. The discontinuous curves in panels d–f indicate a transition from a stable equilibrium (when h exceeds a critical value) to a two-point cycle (when h is below that critical value). The foraging threshold ( f ) had a major impact on the mean densities (Fig. 3), but the exact pattern depended on the maximum depletion. This means that the level of depletion of the tubers by the swans in a particular autumn greatly affected the mean number of tubers available to the swans in the next autumn. Fig. 4 shows the yield taken by the swans for different foraging threshold ( f ), i-values and the
maximum depletion (h). Because the yield is directly related to the tuber production, the effect on the yield is similar to the effect on N*autumn. Fig. 5 demonstrates the yield as a function of tuber winter mortality (m) for different i-values and foraging threshold ( f ). For a wide range of winter mortality, there is barely any effect on N*autumn and N*winter. There is, naturally, a rather strong negative effect of increased winter mortality on the number of sprouting ramets the following spring (N*spring). In Fig. 6, we show the effect of the maximum per capita tuber production (i) and the maximum depletion (h) on the stability of the population, as a phase diagram of ramet density in spring. In general, increasing i is destabilising in the sense
Fig. 3. Mean population density in spring (N*spring = ramet density), autumn (N*autumn =tuber density) and winter (N*winter =tuber density) plotted against the foraging threshold (the tuber density below which no foraging takes place). The maximum depletion (h) is set to 1 (solid curves), 0.8 (dashed curves) or 0.6 (dotted curves). h is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The maximum per capita tuber production (i) is either 5 (a – c), 10 (d – f), or 15 (g –i). Other parameter values are b =0.006 (strength of density-dependence), m =0.2 (the per capita mortality rate of tubers during winter) and w =0.03 g (mean tuber weight). When the tuber density before grazing falls below the foraging threshold (intersects the straight line in panels d –f and indicated by arrows in all panels), no grazing takes place. In the lower panels (g – i), however, the population is cyclic and grazing occurs every second year even though the mean density (N*autumn) is below the foraging threshold.
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Fig. 4. Yield taken by the swans as a function of the foraging threshold ( f ), i.e. the tuber density below which no foraging takes place. The maximum depletion (h) is either 1 (solid curves), 0.8 (dashed curves) or 0.6 (dotted curves). h is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The maximum per capita tuber production (i) is 5 (a), 10 (b), or 15 (c). Other parameter values are b = 0.006 (strength of density-dependence), m =0.2 (the per capita mortality rate of tubers during winter), and w= 0.03 g (mean tuber weight).
that increasing i results in a transition from stable to cyclic and, finally, chaotic dynamics. Increasing h, on the other hand, has a dampening effect on the dynamics. There is no qualitative, and barely any quantitative, difference between the effect on population density at different times of the year.
4. Discussion Since waterbirds consume the whole tuber, herbivory on tubers is in many respects similar to predation. In that sense, we are studying a special case of herbivory, different from partial consumption of leaves and shoots (A, stro¨ m et al., 1990). A decrease in ramet density with increasing grazing, as predicted by our model, has been found in the one study in which ramet density was
measured (Idestam-Almquist, 1996). However, the potential for compensatory tuber production as predicted by the model, has not been observed or suggested before. The predicted increase in tuber density from our model is a consequence of the negative density-dependence in the per capita tuber production. The swans simply remove tubers before the tubers give rise to crowding effects during the reproductive season. In contrast, Anderson and Low (1976) reported a lower tuber density in open plots relative to adjacent exclosures. Both Anderson and Low (1976) and Idestam-Almquist (1996) used exclosures that were present year-round, and thus excluded both leaf- and tuber-eating waterbirds. In our present study we explicitly considered grazing by tubereating swans only. Inclusion of summer grazing would add further complexity to this swan– pondweed interaction. Summer exclosure experi-
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ments in the Lauwersmeer have shown that an increase in grazing by leaf-eating coots (Fulica atra) leads to a reduction of tuber density in the following autumn (Santamarı´a, Unpublished data). Our results show that it is somewhat trivial to conclude that herbivory reduces resource density by measuring density before and just after grazing has occurred, because the mortality can be compensated for by one or several density-dependent processes following it. To understand the potential effects of a source of mortality (e.g. herbivory) on the resource density, the temporal structure of density-dependent events becomes important (A, stro¨ m et al., 1996; Kokko and Lindstro¨ m, 1998; Jonze´ n and Lundberg, 1999). Also the timing of the evaluation of the effects in relation to different processes becomes critical if mortality
and production are seasonal events (Boyce et al., 1999; Jonze´ n and Lundberg, 1999). This illustrates the need to measure how the per capita mortality and production rates vary with density if we want to make progress in our understanding of population dynamics in general and consumer–resource interactions in particular. Unfortunately, this is often the one feature of a plant population that is not investigated during demographic studies (Watkinson, 1980). The model structure presented here represents a framework for evaluating data on demographic rates and examine ramifications for population dynamics (Boyce et al., 1999). In fact, for the kind of data we have got (no time series, but data on seasonal processes) there is simply no other model structure to consider but an explicit seasonal model. There are different ways of modelling sea-
Fig. 5. Mean population density in spring (N*spring = ramet density; panel a), autumn (N*autumn =tuber density; panel b) and winter (N*winter =tuber density; panel c) plotted against per capita mortality rate of tubers during winter (m). Solid curves: i= 5, f= 7; dashed curves: i= 5, f= 14; dashed/dotted curves: i =15, f =7; dotted curves: i= 15, f= 14 (i is the maximum per capita tuber production and f is the foraging threshold, i.e. the tuber density below which no foraging takes place). Other parameter values are b= 0.006 (strength of density-dependence), h= 0.8 (maximum depletion, the slope of the functional response), and w =0.03 g (mean tuber weight).
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Fig. 6. Phase diagram for the population density in spring ( = ramet density). The maximum depletion (h) is the slope of the functional response and approaches the actual fraction of tubers taken when the tuber density before grazing goes to infinity. The foraging threshold ( f ) —the tuber density below which no foraging takes place —is set to 7 g m − 2. Other parameter values are b= 0.006 (strength of density-dependence), m= 0.2 (the per capita mortality rate of tubers during winter), and w =0.03 g (mean tuber weight).
sonality. A common approach is to use differential equations and replace a parameter with a periodic function. That approach was used by Holt and Colvin (1997) who showed that a correct description of seasonality was necessary to reconstruct the observed population dynamics in an African grasshopper. A similar approach was used also by Kokko and Lindstro¨ m (1998) in a harvesting context. We think, however, that including seasonality as discrete events— as in our study—is more intuitive and facilitates the interpretation of data. Under what circumstances a consumer has a stabilising or destabilising effect on a resource has been a matter of debate for quite some time (e.g. Schmitz et al., 1997). The key to understanding has been the functional response, i.e. the per predator predation rate as a function of prey density (Holling, 1959). The functional response offers an attractive possibility to link behavioural ecology and population/community dynamics
(Fryxell and Lundberg, 1998). The functional response used in this study conforms to the optimal functional response, i.e. the classical so-called differential functional response integrated over both foraging time and alternative activities when time is allocated optimally (Abrams, 1982; Sih, 1984; Abrams, 1990; Mitchell & Brown, 1990). If there exists a threshold density, below which no consumption occurs, there always exists a range of densities over which the consumption is stabilising (Mitchell and Brown, 1990). When the yield is only a function of the net energetic gain, the slope of the optimal functional response is predicted to be one over this range. There is more than one possible explanation for a slope less than one (underutilization of rich patches), as was found by Nolet et al. (2001) and used in our study. First, foraging might incur an extra cost, termed the missed opportunity cost of foraging (Mitchell and Brown, 1990). Second, the birds only possess incomplete knowledge about
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their resources (Valone and Brown, 1989). Third, patches of similar quality are spatially grouped (Morgan et al., 1997). Which of the three plays the most important role in our system is impossible to say at the moment. During winter, the tubers suffer from mortality. The different effect of increasing winter mortality on the mean density of ramets (N*spring decreases with increasing m) and tubers (small effect for a wide range of m) again highlights the non-trivial task of evaluating the effect of seasonal population processes. The process of winter mortality, however, deserves further study. Recently, Idestam-Almquist (1996) found a severe effect of waterfowl on fennel pondweed abundance and suggested that waterfowl may stabilise a plant population at a low density. This idea is supported by our study, considering the foraging threshold and maximum depletion found, which tend to have a stabilising effect. In contrast, the swans only depend on fennel pondweed tubers during migration, so other factors than local tuber density are likely to affect swan numbers. The swan dynamic is also operating at a very different (slower) time scale than the tuber population. We thus assumed that the influence of the plant population on the swan population is insignificant. Such an asymmetry of the interaction between consumers and resources is not unusual in many plant– herbivore systems (Fryxell and Lundberg, 1998).
5. Conclusion We have clearly demonstrated the potential importance of explicitly taking seasonality into account when trying to understand how herbivory affects plant dynamics. This is so independent on whether we are building models for scientific or management purposes, or if we are trying to interpret experimental data. This has recently been highlighted in a predation and management context (Boyce et al., 1999), but this line of thinking has, to our knowledge, not yet permeated the herbivory literature. This general conclusion is nicely illustrated by the swan– pondweed system we have studied, where the pondweed seems to be
able to sustain heavy grazing due to compensatory tuber production.
Acknowledgements We are grateful to Wolf Mooij, Marcel Klaassen, Miguel Rodrı´guez-Girone´ s, Anna Ga˚ rdmark and Per Lundberg for invaluable comments and suggestions. Niclas Jonze´ n was financially supported by grants from the Swedish Research Council for Forestry and Agriculture and the Royal Netherlands Academy of Arts and Sciences. This is NIOO-KNAW publication 2830 of the Netherlands Institute of Ecology.
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